Line chart

This simple graph shows data over intervals with connected points

A line chart or line graph is a type of chart which displays information as a series of data points called 'markers' connected by straight line segments.[1] It is a basic type of chart common in many fields. It is similar to a scatter plot except that the measurement points are ordered (typically by their x-axis value) and joined with straight line segments. A line chart is often used to visualize a trend in data over intervals of time – a time series – thus the line is often drawn chronologically. In these cases they are known as run charts.[2]

History

Some of the earliest known line charts are generally credited to Francis Hauksbee, Nicolaus Samuel Cruquius, Johann Heinrich Lambert and William Playfair.[3]

Example

In the experimental sciences, data collected from experiments are often visualized by a graph. For example, if one were to collect data on the speed of a body at certain points in time, one could visualize the data by a data table such as the following:

Graph of Speed Vs Time
Elapsed Time (s) Speed (m s−1)
0 0
1 3
2 7
3 12
4 20
5 30
6 45.6

The table "visualization" is a great way of displaying exact values, but can be a poor way to understand the underlying patterns that those values represent. Because of these qualities, the table display is often erroneously conflated with the data itself; whereas it is just another visualization of the data.

Understanding the process described by the data in the table is aided by producing a graph or line chart of Speed versus Time. Such a visualisation appears in the figure to the right.

Mathematically, if we denote time by the variable , and speed by , then the function plotted in the graph would be denoted indicating that (the dependent variable) is a function of .

Best-fit

A parody line graph published in 1919.

Charts often include an overlaid mathematical function depicting the best-fit trend of the scattered data. This layer is referred to as a best-fit layer and the graph containing this layer is often referred to as a line graph.

It is simple to construct a "best-fit" layer consisting of a set of line segments connecting adjacent data points; however, such a "best-fit" is usually not an ideal representation of the trend of the underlying scatter data for the following reasons:

  1. It is highly improbable that the discontinuities in the slope of the best-fit would correspond exactly with the positions of the measurement values.
  2. It is highly unlikely that the experimental error in the data is negligible, yet the curve falls exactly through each of the data points.

In either case, the best-fit layer can reveal trends in the data. Further, measurements such as the gradient or the area under the curve can be made visually, leading to more conclusions or results from the data.

A true best-fit layer should depict a continuous mathematical function whose parameters are determined by using a suitable error-minimization scheme, which appropriately weights the error in the data values. Such curve fitting functionality is often found in graphing software or spreadsheets. Best-fit curves may vary from simple linear equations to more complex quadratic, polynomial, exponential, and periodic curves.[4]

See also

References

  1. ↑ Burton G. Andreas (1965). Experimental psychology. p.186
  2. ↑ Neil J. Salkind (2006). Statistics for People who (think They) Hate Statistics: The Excel Edition. page 106.
  3. ↑ Michael Friendly (2008). "Milestones in the history of thematic cartography, statistical graphics, and data visualization". pp 13–14. Retrieved 7 July 2008.
  4. ↑ "Curve fitting". The Physics Hypertextbook.
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